Parameters Identification and Synchronization of Chaotic Delayed Systems Containing Uncertainties and Time-Varying Delay

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme

Chaos control and synchronization of a novelchaotic system based upon adaptive control algorithm

Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical) adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive Control and Synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov Direct Method, the Adaptive Control Techniques are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive Control Law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive Controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using mathematica 9

Free Energy, Value, and Attractors

It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable) states they expect to encounter

Oscillations in microvascular flow:their relationship to tissue oxygenation, cellular metabolic function and their diagnostic potential for detecting skin melanoma - clinical, experimental and theoretical investigations

Tumour vasculature is known to be inefficient and abnormal due to poorly regulated angiogenesis during tumour growth. This leads to irregular patterns of blood flow which are spatially and temporally heterogeneous. Many investigations into the characteristics of tumours are invasive and performed on animal models. However, continuous technological and theoretical advancement is leading to the use of non-invasive imaging techniques, providing in vivo information on humans. Here, data recorded using laser Doppler flowmetry (LDF) in malignant melanoma and control lesions are analysed using techniques designed for application to non-stationary, time-varying data. Many studies utilising LDF have previously revealed increased blood flow in malignant lesions, but very little attention has been paid to the dynamics of this blood flow, or how it changes over time. As it has been demonstrated previously that the oscillations observed within blood flow data are physiologically significant, failure to extract these characteristics loses information about the underlying dynamical system from which the blood flow data were recorded. Significant differences in blood flow dynamics are revealed and used in the development of a diagnostic test for melanoma. In addition to the characterization of the blood flow dynamics in melanoma, possible causes for the observed changes are investigated and related to two widely observed characteristics of cancer, intermittent hypoxia and altered cellular energy metabolism. The former is explored through the analysis of blood flow and oxygenation data recorded during dry static apnoea, whilst the latter is modelled using coupled phase oscillators

Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo

Dynamics of an Ocean Energy Harvester

<p>Ocean-based wireless sensor networks serve many important purposes ranging from tsunami early warning to anti-submarine warfare. Developing energy harvesting devices that make these networks self-sufficient allows for reduced maintenance cost and greater reliability. Many methods exist for powering these devices, including internal batteries, photovoltaic cells and thermoelectric generators, but the most reliable method, if realized, would be to power these devices with an internal kinetic energy harvester capable of reliably converting wave motion into electrical power. Designing such a device is a challenge, as the ocean excitation environment is characterized by shifting frequencies across a relatively wide bandwidth. As such, traditional linear kinetic energy harvesting designs are not capable of reliably generating power. Instead, a nonlinear device is better suited to the job, and the task of this dissertation is to investigate the behaviors of devices that could be employed to this end.</p><p>This dissertation is motivated by the design and analysis of an ocean energy harvester based on a horizontal pendulum system. In the course of investigating the dynamics of this system, several discoveries related to other energy harvesting systems were made and are also reported herein. It is found that the most reliable method of characterizing the behaviors of a nonlinear energy harvesting device in the characteristically random forcing environment of the ocean is to utilize statistical methods to inform the design of a functional device. It is discovered that a horizontal pendulum-like device could serve as an energy harvesting mechanism in small self-</p><p>sufficient wireless sensor buoys if properly designed and if the proper transduction mechanisms are designed and employed to convert the mechanical energy of the device into electrical power.</p>Dissertatio

Aspects of Invariant Manifold Theory and Applications

Recent years have seen a surge of interest in "data-driven" approaches to determine the equations governing complex systems. Yet in spite of modern computing advances, the high dimensionality of many systems --- such as those occurring in biology and robotics --- renders direct machine learning approaches infeasible. This dissertation develops tools for the experimental study of complex systems, based on mathematical concepts from dynamical systems theory. Our approach uses the fact that parsimonious assumptions often lead to strong insights from dynamical systems theory; such insights can be leveraged in learning algorithms to mitigate the “curse of dimensionality” and make these algorithms practical. Our first contribution concerns nonlinear oscillators. Oscillators are ubiquitous in nature, and usually associated with the existence of an "asymptotic phase" which governs the long-term dynamics of the oscillator. We show that asymptotic phase can be expressed as a line integral with respect to a uniquely defined closed differential 1-form, and provide an algorithm for estimating this "ToF" from observational data. Unlike all previously available data-driven phase estimation methods, our algorithm can: (i) use observations that are much shorter than a cycle; (ii) recover phase within the entire region for which data convergent to the limit cycle is available; (iii) recover the phase response curves (PRC-s) that govern weak oscillator coupling; (iv) show isochron curvature, and recover nonlinear features of isochron geometry. Our method may find application wherever models of oscillator dynamics need to be constructed from measured or simulated time-series. Our next contribution concerns locomotion systems which are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that in the ``Stokesian'' (viscous; zero Reynolds number) limit, the motion is governed by a reduced order "connection'' model that describes how body shape change produces motion for the body frame with respect to the world. In the "perturbed Stokes regime'' where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer connection-like. We derive this model using results from noncompact NHIM theory in a singular perturbation framework. Using a normal form derived from theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a "gait") directly from observational data of shape and body motion. Our algorithm has applications to the study of optimality of animal gaits, and to hardware-in-the-loop optimization to produce gaits for robots. Finally, we make fundamental contributions to NHIM theory: we prove that the global stable foliation of a NHIM is a $C^0$ disk bundle, and we prove that the dynamics restricted to the stable manifold of a compact inflowing NHIM are globally topologically conjugate to the linearized transverse dynamics at the NHIM restricted to the stable vector bundle. We also give conditions ensuring $C^k$ versions of our results, and we illustrate the theory by giving applications to geometric singular perturbation theory in the case of an attracting critical manifold: we show that the domain of the Fenichel Normal Form can be extended to the entire global stable manifold, and under additional nonresonance assumptions we derive a smooth global linear normal form.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147642/1/kvalheim_1.pd